Nth Root Calculator
Calculate any root of any number — square, cube, fourth or a fractional degree — with the result checked by raising it back to that power.
How to use it
- Enter the number and the degree of the root you want.
- Odd roots of negative numbers work; even roots of negatives have no real answer.
- The square and cube roots are always shown for comparison.
Examples
| ∛27 | 3 |
| ⁴√81 | 3 |
| ∛−8 | −2 |
The nth root of a number is whatever value, raised to the power n, gives that number back. It generalises the familiar square root (n = 2) and cube root (n = 3) to any degree, including fractional degrees, using ⁿ√x = x^(1 ÷ n).
Cube roots and volume
Cube roots answer 'what side length gives this volume?'. A storage cube needs to hold 64 litres (64,000 cm³); the side length is ∛64,000 = 40 cm. The same logic works in reverse for any container problem where volume is known and a dimension is not.
Odd vs even roots of negative numbers
| Root degree | Negative input | Real answer? |
|---|---|---|
| Odd (3, 5, 7…) | ∛−8 | Yes — −2, because (−2)³ = −8 |
| Even (2, 4, 6…) | ⁴√−16 | No real answer — no real number raised to an even power is negative |
Questions people ask
Why is there no real fourth root of a negative number?
Any real number raised to an even power is positive, so nothing real can give a negative result. Odd powers keep the sign, which is why cube roots of negatives are fine.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026